${\sqrt[3]{2160} = \text{?}}$
$\sqrt[3]{2160}$ is the number that, when multiplied by itself three times, equals $2160$ First break down $2160$ into its prime factorization and look for factors that appear three times. So the prime factorization of $2160$ is $2\times 2\times 2\times 2\times 3\times 3\times 3\times 5$ Notice that we can rearrange the factors like so: $2160 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 5 = (2\times 2\times 2) \times (3\times 3\times 3) \times 2\times 5$ So $\sqrt[3]{2160} = \sqrt[3]{2\times 2\times 2} \times \sqrt[3]{3\times 3\times 3} \times \sqrt[3]{2\times 5}$ $\sqrt[3]{2160} = 2\times 3 \times \sqrt[3]{2\times 5}$ $\sqrt[3]{2160} = 6 \sqrt[3]{10}$